Asymptotic chaos (Q1077780)

The aim of the present work is to illustrate how, in a physical system with a triple instability, chaos occurs when the parameters are chosen to be arbitrarily close to the simultaneous onset of the three instabilities. The article provides a list of normal forms of ordinary differential equations describing the dynamics of systems in conditions near to three instabilities. A proof is sketched using normal form theory [\textit{V. I. Arnol'd}, Usp. Mat. Nauk 27, No.5(167), 119-184 (1972; Zbl 0248.58001)]. The numerical investigation of this asymptotic normal form strongly suggests that chaotic behavior occurs as close as possible to the onset of the triple instability.